Negligible function

In mathematics, a negligible function is a function${\displaystyle \mu :\mathbb {N} \to \mathbb {R} }$ such that for every positive integerc there exists an integer N_c such that for all n > N_c,

${\displaystyle |\mu (n)|<{\frac {1}{n^{c}}}.}$

Equivalently, the following definition may be used. A function ${\displaystyle \mu :\mathbb {N} \to \mathbb {R} }$ is negligible, if for every positive polynomial poly(·) there exists an integer N_poly > 0 such that for all n > N_poly

${\displaystyle |\mu (n)|<{\frac {1}{\operatorname {poly} (n)}}.}$